World number one Selby lost 4-3 to Liang Wenbo in a match which finished at 1.10am.
Earlier in the day Trump, last year's runner-up, was beaten 4-1 by Noppon Saengkham of Thailand, who is ranked 58th in the world.
It was the same score as Ding, China's world number four, was beaten by world number 69 Liam Highfield.
World number three Trump, quoted by worldsnooker.com, said: "I got what I deserved, I played terrible in both of my games here (in round one he beat Duane Jones 4-3).
"This is one of the tournaments I wanted to do well at, so it's disappointing to lose. I tried until the end today but the confidence just wasn't there."
Neil Robertson was another big-name casualties on day three, despite making three centuries. After five frames Robertson led 3-2 and had a 100% pot success rate having fired runs of 100, 100 and 130. But world number 100 Burns, who earlier had breaks of 85 and 106, took the last two frames with 75 and 47.
Preston’s Burns said: “It’s very pleasing to beat one of the best players in the world and play that well. I don’t play on the TV tables too often so it’s nice to get out there and perform well.”
Ronnie O'Sullivan progressed to the last 32 in comfortable fashion as he saw off Graeme Dott 4-0, scoring a top break of 106 which was his 60th century of the season and the 934th of his career.
The Rocket, who will next play David Grace, said: "I have always been into my health, fitness and running. Because of injuries I started to put a bit of weight on so I decided to work with a nutritionist. The benefit of that was feeling good in myself and having more energy. I take my diet more seriously now than I have ever done. I have massively changed my diet, learned about it and educated myself."
Home favourite Mark Williams kept up his hopes of winning a third ranking title of the season as he beat India’s Aditya Mehta 4-3, having edged a marathon 73-minute frame.
The only other Welshman in the third round is Matthew Stevens, who beat Scott Donaldson 4-2.
Defending champion Stuart Bingham ended the hopes of Welsh 16-year-old Jackson Page, winning 4-2 with top breaks of 77, 92 and 65.
All the results below...
WEDNESDAY FEBRUARY 28
Morning session (1000 GMT)
Second Round (Best of 7 frames)
- Peter Ebdon 4-1 Anthony Hamilton
- Fang Xiongman 4-2 Chen Zifan
- Ding Junhui 1-4 Liam Highfield
- Chris Wakelin 4-2 Andrew Higginson
- James Wattana 4-2 Michael Holt
- Craig Steadman 4-2 Thepchaiya Un-Nooh
- Noppon Saengkham 4-1 Judd Trump
- David Grace 4-0 Jak Jones
Afternoon session (1300 GMT)
Second Round (Best of 7 frames)
- Scott Donaldson 2-4 Matthew Stevens
- Ricky Walden 3-4 Martin Gould
- Ronnie O'Sullivan 4-0 Graeme Dott
- Luca Brecel 1-4 Mike Dunn
- Xu Si 4-2 Michael Georgiou
- Nigel Bond 4-3 Ali Carter
- Sam Craigie 4-1 Kurt Maflin
- Robbie Williams 4-0 Ian Preece
- Stuart Bingham 4-2 Jackson Page
- Jamie Jones 1-4 Akani Songsermsawad
- Mark Allen 4-1 Soheil Vahedi
- Oliver Lines 2-4 Yu De Lu
- Ben Woollaston 4-3 Anthony McGill
- Neil Robertson 3-4 Ian Burns
- Gerard Greene 4-3 Stuart Carrington
Evening session (1900 GMT)
Second Round (Best of 7 frames)
- Kurt Dunham 2-4 Yan Bingtao
- Tom Ford 0-4 Barry Hawkins
- Aditya Mehta 3-4 Mark Williams
- Rory McLeod 0-4 Kyren Wilson
- Lyu Haotian 2-4 Jack Lisowski
- Dominic Dale 2-4 John J Astley
- Gary Wilson 4-3 Daniel Wells
- Stephen Maguire 1-4 John Higgins
- Liang Wenbo 4-3 Mark Selby
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